Working on the badge dimensions, I took a digital caliper and measured a few bits on the earpiece. It's roughly 46.51 x 16.09 mm and shaped like a surfboard. The narrow end is about 5.14mm tall while the other is about 12.38mm. The microphone is encased in rubber. It's about 12.90 x 16.26mm and 7.30mm deep. I decided to mount it at the top of badge where it's behind the face and not visible. Depth will be fine because the battery is deeper.
I'm not much of a CAD kind of guy so I fired up Tinkercad and imported the STL I found. I carved out a few boxes and then rounded the corners with four ovals of the proper dimension. I then subtracted this from the back of the badge making sure none of the negative space popped out to the front. I then carved out the space for the microphone and a 1.2 mm groove for wires between the main circuit board and the mike. Not sure yet about speaker placement.
I'm now printing the updated badge to test fit the components.